K‐theory of regular compactification bundles

V. Uma

Mathematische Nachrichten, 2022, vol. 295, issue 5, 1013-1034

Abstract: Let G be a split connected reductive algebraic group. Let E⟶B$\mathcal {E}\longrightarrow \mathcal {B}$ be a G×G$G\times G$‐torsor over a smooth base scheme B$\mathcal {B}$ and X be a regular compactification of G. We describe the Grothendieck ring of the associated fibre bundle E(X):=E×G×GX$\mathcal {E}(X):=\mathcal {E}\times _{G\times G} X$, as an algebra over the Grothendieck ring of a canonical toric bundle over a flag bundle over B$\mathcal {B}$. These are relative versions of the corresponding results on the Grothendieck ring of X in the case when B$\mathcal {B}$ is a point, and generalize the classical results on the Grothendieck rings of projective bundles, toric bundles and flag bundles.

Date: 2022
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